Liquidation Games with Market Dropout and No Round Trips

Summary

The paper studies portfolio liquidation games in which a trader exits the market once their position reaches zero. This absorption rule rules out round-trip trading and is framed as a no-statistical-arbitrage condition. In a model containing only sellers, the authors prove that absorption is equivalent to a short-selling constraint. They analyze both mean-field games, which represent many interacting participants through an aggregate population, and finite-player games.

Equilibria in both settings are characterized through a nonlinear higher-order integral equation with an endogenous terminal condition. The paper proves that the equation has a unique solution, yielding unique equilibria for the mean-field and finite-player games. It also establishes convergence of finite-player equilibria to the mean-field equilibrium and illustrates how the dropout constraint changes equilibrium trading rates. The brief description does not provide the model’s specific market-impact assumptions or quantitative size of those rate changes.

Key ideas

• Players leave the market when their position reaches zero, so round trips are excluded.
• In the all-seller model, the absorption rule is equivalent to a short-selling constraint.
• Equilibria are characterized by a nonlinear integral equation with an endogenous terminal condition.
• The authors prove uniqueness of equilibria for both mean-field and finite-player games.
• Finite-player equilibria converge to the mean-field equilibrium, and dropout affects trading rates.

Tags

# Mean-Field Liquidation Games with Market Drop-out


# Mean-Field Liquidation Games with Market Drop-out









We consider a novel class of portfolio liquidation games with market drop-out ("absorption"). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular round-trips are not admissible. This can be viewed as a no statistical arbitrage condition. In a model with only sellers we prove that the absorption condition is equivalent to a short selling constraint. We prove that equilibria (both in the mean-field and the finite player game) are given as solutions to a non-linear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium in the MFG and the existence of a unique equilibrium in the $N$-player game. We establish the convergence of the equilibria in the finite player games to the obtained mean-field equilibrium and illustrate the impact of the drop-out constraint on equilibrium trading rates.

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